Brave Lucina

First and foremost, she is built for support, but can fight to kill red/dragons, and also can be an emergency hero if the main hero has been killed.

This specific build is to get Altina to 75 atk

NOTE: This build will be updated when they decide to put Distant Guard 3 in the Sacred Seal slot. I...honestly don't know why they haven't done it yet if fehstuff of all sites has it done already.
ALSO NOTE: This build is taking into account that the Brave!Lucina has a Def boon and is at +10 merges and +10 Dragonflowers, as well as having an S-Rank Summoner Support. Without counting bonuses, her statline is 55 HP, 58 Atk, 44 Spd, 42 Def, 27 Res.

In my opinion, I think this is Brave!Lucina's best Support build with Geirskogul (at this time). Below are the pros and cons that I know of with this build so far.

Pros:
1) Anti-dragon effectiveness. With Geirskogul's refinement she gains this effect, and with Ruptured Sky she can increase her damage to them even further very quickly. Atk/Spd Push 4 increases her Atk/Spd to 65/51, making her offensive presence just as dangerous as her supportive presence (especially to dragons).
2) Quality tankiness. Thanks to her high Spd combining with Atk/Spd Push 4, Close Call 3 has 51 Spd to work with, meaning that any foe with 41 or less Spd will deal 40% less damage to her (discounting any Spd debuffs they might inflict).
3) High offensive presence. Like it was explained in Pros 1, her offensive presence is pretty high. With 65/51 Atk/Spd, she doubles anything with 46 or less Spd, and with Ruptured Sky at 2 cooldown she'll always be able to trigger it under normal circumstances. Also, due to Close Call, any unit with 41 or less Spd that has the Atk to deal real damage to her despite the damage reduction will inherently take more damage from Ruptured Sky.
4) God-Tier Support. This is really what you're here for. I've been talking about her fighting others by herself, but what you're really using this build for is her role as a Support. Her refined Geirskogul gives All+3 and super-charging during the Enemy Phase to allies within 2 spaces, and with both Close and Distant Guard she also provides those allies with a dual phase Def/Res+4 during combat (effectively giving her Drive-distance allies Def/Res+7 during the Enemy Phase).
5) Great positional utility. With Close Call having Hit and Run built into it, and her Geirskogul/dual Guards having their generous Drive range, it's quite easy to set herself and her team up both offensively and defensively. You can very easily switch Reciprocal Aid for Reposition and the like; the reason I won't here is purely for healing her HP for Atk/Spd Push 4, but this CAN be easily solved by putting a Healer or pseudo-Healer on her team.
6) Godly dueling presence due to Close Call. This is more of a continuation of both Pros 2 and 3, but I felt it had to be said. She can actually out-duel an unmerged +Atk Winter!Ephraim that's initiating on her with his natural skills if she has Ruptured Sky charged by her first attack. Because of Close Call, she can actually tank his Dragon Fang (which is even more powerful due to him having 71 Atk during combat), and only take 38 damage from it, and on her counterattack he'll take 53 damage (if she activates Ruptured Sky at this time) and get OHKO'd. Yes, he's umerged...but this is a Support build and she's capable of out-dueling the guy with the highest possible natural Atk in the game so far. I think that's worth something.

Cons:
1) No Distant Counter. Atk/Spd Push 4 is necessary to maximize the effectiveness of both Ruptured Sky and Close Call, but this leaves her without the ability to counterattack against ranged foes during the Enemy Phase. This leaves her especially vulnerable to Tomes and Wrathful Staffers, and also daggers to an extent.
2) Low magical bulk. Close Call can only mitigate so much damage, and 82 magical bulk isn't all that much when you have so many great magic-based Nukes present in the game. Even some of the very dragons she one-shots have a great chance at destroying her during the Enemy Phase if you aren't careful with her positioning beforehand.
3) No defense against debuffs or defensive Bonus Doublers. She's capable of taking advantage of offensive Bonus Doublers due to Ruptured Sky, but defensive strategies leave her doing less than she wants. Since she uses Close Call in this build instead of a Lull or Dull skill, she has to make do with brute force or just simply leaving it to her allies to finish the job. On the debuffs side, Close Call's own effect falls off when faced with Spd debuffs (though thankfully this is largely mitigated by Atk/Spd Push 4 being in-combat and not a field bonus that can be Panic'd). Res debuffs are also a massive concern due to her sub-optimal magical bulk.
4) Green Tanks. Even gods can only do so much, and Brave!Lucina (despite not actually being a goddess) is no different. If she faces a foe that she just can't deal damage to regardless of her offensive statline, she'll need to rely on her allies to take them down for her. And though the synergy of Close Call and Ruptured Sky is really amazing, tanks with lower Atk make Ruptured Sky have less usage than she needs against said foes. Having a Red ally that can easily deal with tanky Green foes, magic or not, is a must for her.
5) Geirskogul's reliance on physical allies. This is old news with anyone using Brave!Lucina, but I felt it needed to be mentioned. While her magical allies will be affected by the dual Guards, they won't be able to be affected by Geirskogul's effect. If you're going to have her work with a magical ally, make sure they can work fairly independently from the rest of the team (or at least independently from her).

There are probably a lot more pros and cons than what I've listed, and I'll be coming back anyhow once Gamepress adds Distant Guard to the list of Sacred Seals, so expect updates. Note, however, that I've permanently left the Discord server and will NOT be available for advice because the mods there are trash and their rules are worse than trash.
If anyone wants to discuss Brave!Lucina with me, I go by the same name on here as I do on SerenesForest. I don't think I can actually set up a topic dedicated to Brave!Lucina on there without it getting removed, but feel free to message me there regardless.

Geirskögul (+Eff) +3 HP +16 Mt.
Effective against dragon foes. Grants Def+3. Grants Atk/Spd/Def/Res+3 to sword, lance, axe, bow, dagger, or beast allies within 2 spaces during combat, and if foe initiates combat against those allies, grants Special cooldown charge +1 per attack to those allies. (Only highest value applied. Does not stack.)

With her new fantastic refine, Brave Lucina becomes a fantastic support unit for non-magical allies. Possibly becoming one of the best support units in the game, due to her massive +3 buffs to all non-magical allies within 2 spaces as well as effectively giving them steady breath effect as well. While she has dragon effectiveness and great stats overall, Brave Lucina still wants to focus on being an arena support or just a support unit in general. Fury 4 is significant here as it allows Brave Lucina to hit high atk, spd & def stats which lets her soak Chill skills for her allies, while allowing her to be a monster in combat if ever needed. Chill skills in both B & seal allows her allies to deal with enemies easier and Close Guard provides even more buffs for her allies. The choice of Close Guard vs Distant Guard depends on your team comp, just like the rally skill she wants to take. While she can be running Link skills and movement skills, those only benefit one ally and can be tricky to use while double chill is consistent and benefits all her allies.

Boon: +Def (if at +0, her best bane in this build is -Res)
Weapon: Slaying Lance+ (+Spd)
Support: Reciprocal Aid
Special: Aether
Passive A: Steady Breath, Atk/Def Bond 3, Spd/Def Bond 3 (the Bond skills if she has an ally with Infantry Breath 3)
Passive B: Wrath 3 / Guard 3
Passive C: Atk or Spd Smoke 3, an Infantry skill, or a Wave or Tactic skill (preferably Wave unless she is used on a Mixed team)
Seal: Darting Stance 3 / Close Def 3 / Panic Ploy 3 / Quick Riposte 3
Summoner Support: Absolutely
Ally Support: Red unit for protecting her against Green units, or Green unit so she can protect them. Someone that can counter enemies like Hector or Grima would be great. If she has an ally with Infantry Breath (like Yarne), she can use a different A Passive (preferably a Bond skill to take advantage of the fact she needs to be adjacent to that ally to gain the Breath).

Super-sustain pseudo-Healer Brave!Lucina. With Slaying Lance+ (+Spd), this Brave!Lucina can get up to 39 Spd (43 at +10 in merges, then 45 at +10 dragonflowers), and due to the combination of it and her speed with Steady Breath, she can fully charge and activate an originally 5-cooldown skill like Aether in a single instance of battle. Reciprocal Aid is a great option for proccing Wrath. Obviously, her Special is Aether which is amazing at both damage and sustain. Activating this each time she battles an enemy is pretty brutal to a lot of enemies.
Her A skill is Steady Breath. While this does force her niche into becoming an Enemy Phase unit, a Def boon lets her reach up to 35 Def with its effect...and with a neutral base 34 Atk (48 with the weapon) she'll be retaliating pretty hard after tanking your opponent's attacks. Unfortunately, this Def increase does nothing against Res-targeting units (especially Green ones), so keep her away from them unless she's in a winning battle.
For her B skill, either Wrath 3 or Guard 3 are your best placements. Wrath 3 lets her charge Aether even faster and increases its damage by 10 (and therefore potential healing by 5), while Guard 3 gives her some safety against units that can deal some nice damage to her with their Specials.
Spd Smoke 3 is her safest option for her C skill, making it harder for consecutive opponents to double her (and making it easier for her to double them in return). Otherwise, her best options should be based on the team she's on.
As for her seal, Panic Ploy 3 is my favorite to use against Emblem teams. Darting Stance 3, however, is a lot better so as to increase her Spd. For a bit more Def/Res against her counterable enemies, Close Def 3 is equally if not more usable.
For your Ally Support, be sure to take an ally that can either help or be helped from Brave!Lucina's status as a lance unit. A strong unit that has lower (current) HP than she does will be able to be restored to full health from her Reciprocal Aid depending on her HP at the time, and she can make use of Steady Breath/Aether to get back up to full health for another pseudo-heal. A unit that can stand alongside her on the front lines, preferably one with a Distant Counter weapon/A Passive like Legendary!Ike, is also perfect for her (it also helps that he's a sword user with DC built into his weapon, so he can protect her against axe users like Arthur AND Tome users like Nino thanks to his natural Warding Breath).